Bias correction for lithography

ABSTRACT

Methods include inputting an array of pixels, where each pixel in the array of pixels has a pixel dose. The array of pixels represents dosage on a surface to be exposed with a plurality of patterns, each pattern of the plurality of patterns having an edge. A target bias is input. An edge of a pattern in the plurality of patterns is identified. For each pixel which is in a neighborhood of the identified edge, a calculated pixel dose is calculated such that the identified edge is relocated by the target bias. The array of pixels with the calculated pixel doses is output. Systems for performing the methods are also disclosed.

RELATED APPLICATIONS

This application is a divisional of U.S. patent application Ser. No.15/631,331, filed on Jun. 23, 2017 and entitled “Bias Correction forLithography”; which claims priority to U.S. Provisional PatentApplication No. 62/355,869, filed on Jun. 28, 2016 and entitled “BiasCorrection in Charged Particle Beam Lithography”; all of which arehereby incorporated by reference.

BACKGROUND OF THE DISCLOSURE

In the production or manufacturing of semiconductor devices, such asintegrated circuits, optical lithography may be used to fabricate thesemiconductor devices. Optical lithography is a printing process inwhich a lithographic mask or photomask or reticle is used to transferpatterns to a substrate such as a semiconductor or silicon wafer tocreate the integrated circuit (I.C.). Other substrates could includeflat panel displays, holographic masks or even other reticles. Whileconventional optical lithography uses a light source having a wavelengthof 193 nm, extreme ultraviolet (EUV) or X-ray lithography are alsoconsidered types of optical lithography in this application. The reticleor multiple reticles may contain a circuit pattern corresponding to anindividual layer of the integrated circuit, and this pattern can beimaged onto a certain area on the substrate that has been coated with alayer of radiation-sensitive material known as photoresist or resist.Once the patterned layer is transferred the layer may undergo variousother processes such as etching, ion-implantation (doping),metallization, oxidation, and polishing. These processes are employed tofinish an individual layer in the substrate. If several layers arerequired, then the whole process or variations thereof will be repeatedfor each new layer. Eventually, a combination of multiples of devices orintegrated circuits will be present on the substrate. These integratedcircuits may then be separated from one another by dicing or sawing andthen may be mounted into individual packages. In the more general case,the patterns on the substrate may be used to define artifacts such asdisplay pixels, holograms, directed self-assembly (DSA) guard bands, ormagnetic recording heads. Conventional optical lithography writingmachines typically reduce the photomask pattern by a factor of fourduring the optical lithographic process. Therefore, patterns formed onthe reticle or mask must be four times larger than the size of thedesired pattern on the substrate or wafer.

SUMMARY OF THE DISCLOSURE

In some embodiments, a method includes inputting an array of pixels,where each pixel in the array of pixels has a pixel dose. The array ofpixels represents dosage on a surface to be exposed with a plurality ofpatterns, each pattern of the plurality of patterns having an edge. Atarget bias is input. An edge of a pattern in the plurality of patternsis identified. For each pixel which is in a neighborhood of theidentified edge, a calculated pixel dose is calculated such that theidentified edge is relocated by the target bias. The array of pixelswith the calculated pixel doses is output.

In some embodiments, a method includes inputting a plurality of patternsto be exposed on a surface, where each pattern has an edge. The methodalso includes inputting a target bias, and rasterizing the plurality ofpatterns to create an array of pixels, where each pixel in the array ofpixels represents an exposure dosage. Dosages of pixels in the array ofpixels are calculated, where the calculated dosages relocate the edge ofa pattern in the plurality of patterns. The relocation is based on thetarget bias. The array of pixels is output, including the calculatedpixel dosages.

In some embodiments, a system for biasing shapes to be written onto asurface includes a device configured to input an array of pixels. Eachpixel comprises a pixel dose, and the array of pixels represents dosageon a surface to be exposed with a plurality of patterns. Each pattern ofthe plurality of patterns has an edge. The system also includes a deviceconfigured to identify an edge of a pattern in the plurality ofpatterns; a device configured to calculate a calculated pixel dose forpixels which are in a neighborhood of the identified edge, so that theidentified edge is relocated by a target bias; and a device configuredto output the array of pixels with the calculated pixel doses. Thesystem can also include a device configured to determine the dosages inthe pixel array, using a set of geometric shapes. In some embodiments,the system can also include a device configured to expose the surfacewith the outputted array of pixels. The device configured to calculatethe pixel doses may operate simultaneously with the device configured toexpose the surface, in an inline fashion. The device configured toexpose the surface may comprise multiple beams.

In some embodiments, a system includes a device configured to expose apattern onto a resist-coated surface using an electron beam, and adevice configured to compute a constant distance bias. The deviceconfigured to expose may expose the resist with multiple beams. Thedevice configured to expose and the device configured to compute mayoperate in an inline fashion. The device configured to compute maycomprise a graphics processing unit (GPU).

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates an example of a variable shaped beam (VSB) chargedparticle beam system as known in the art.

FIG. 2 illustrates an example of an electro-optical schematic diagram ofa multi-beam exposure as known in the art.

FIG. 3A illustrates an example of a rectangular shot.

FIG. 3B illustrates an example of a circular character projection shot.

FIG. 3C illustrates an example of a trapezoidal shot.

FIG. 3D illustrates an example of a dragged shot.

FIG. 3E illustrates an example of a shot which is an array of circularpatterns.

FIG. 3F illustrates an example of a shot which is a sparse array ofrectangular patterns.

FIG. 4 illustrates an example of a multi-beam charged particle beamsystem as known in the art.

FIG. 5 illustrates an example pattern undergoing a positive bias, asknown in the art.

FIG. 6 illustrates geometric biasing as known in the art.

FIG. 7 describes simulation setup conditions for a simulation of dosebiasing as known in the art.

FIG. 8 presents the results of the simulation of FIG. 7.

FIG. 9 illustrates dosage profiles for the simulation of dose biasing ofFIG. 7.

FIG. 10 is a close-up view of a portion of the graph of FIG. 9.

FIG. 11 illustrates a pattern to be rasterized, in accordance withembodiments of the present disclosure.

FIG. 12A illustrates rasterization of the pattern of FIG. 11 into atwo-dimensional pixel dosage array in accordance with embodiments of thepresent disclosure.

FIG. 12B illustrates a pixel dosage array of FIG. 12A with a calculatededge.

FIG. 13A illustrates the pixel dosage array of FIG. 12A with gradientsfrom the calculated edge.

FIG. 13B illustrates dosages of the pixel array of FIG. 12A, afterrelocation of the edge by a target bias amount.

FIG. 14 illustrates a pixel dosage array and a calculated line-endpattern, in accordance with some embodiments.

FIG. 15 illustrates the pixel dosage array of FIG. 14 after biasing theline-end pattern.

FIG. 16 illustrates the pixel dosage array of FIG. 15 after dosageenhancement to improve dose margin.

FIG. 17 is a conceptual flow diagram of a method for pattern biasingusing a pixel dosage array, in accordance with some embodiments.

FIG. 18 illustrates a computing hardware device used in accordance withembodiments of the present methods.

DETAILED DESCRIPTION OF THE EMBODIMENTS

Methods and systems are presented for biasing the dimensions of patternsto be exposed onto a surface. The methods improve the ability to produceconstant distance biasing for edges of a pattern, and improve theefficiency of biasing computations compared to conventional methods. Themethods use an array of pixels that represent dosages, to identify theedge of the pattern and relocate the edge to achieve a target bias. Insome embodiments, dose margin can also be enhanced as part of thebiasing operations. In performing the biasing, dosage calculations canbe performed using dosage data only for pixels neighboring the edge. Thecalculations of the present methods may be performed in an inlinefashion with exposing the patterns on a surface.

The present disclosure is related to lithography, and more particularlyto the design and manufacture of a surface which may be the surface of areticle, a wafer, or any other surface, using charged particle beamlithography. Although embodiments shall be described in terms of asemiconductor wafer or a photomask, the methods and systems describedherein can also be applied to other components used in the manufacturingof semiconductor devices. The embodiments may also be applied to themanufacturing of various electronic devices such as flat panel displays,micro-electromechanical systems, and other microscopic structures thatrequire precision by electron beam writing. Accordingly, a reference toshots being delivered onto a surface shall apply to, for example, asurface of a semiconductor wafer, or a surface of a reticle orphotomask.

Lithography Systems

Referring now to the drawings, wherein like numbers refer to like items,FIG. 1 illustrates an embodiment of a lithography system, such as acharged particle beam writer system, in this case an electron beamwriter system 10, that employs a variable shaped beam (VSB) tomanufacture a surface 12. The electron beam writer system 10 has anelectron beam source 14 that projects an electron beam 16 toward anaperture plate 18. The plate 18 has an aperture 20 formed therein whichallows the electron beam 16 to pass. Once the electron beam 16 passesthrough the aperture 20 it is directed or deflected by a system oflenses (not shown) as electron beam 22 toward another rectangularaperture plate or stencil mask 24. The stencil 24 has formed therein anumber of openings or apertures 26 that define various simple shapessuch as rectangles and triangles. Each aperture 26 formed in the stencil24 may be used to form a pattern in the surface 12 of a substrate 34,such as a silicon wafer, a reticle or other substrate. An electron beam30 emerges from one of the apertures 26 and passes through anelectromagnetic or electrostatic reduction lens 38, which reduces thesize of the pattern emerging from the aperture 26. In commonly availablecharged particle beam writer systems, the reduction factor is between 10and 60. The reduced electron beam 40 emerges from the reduction lens 38and is directed by a series of deflectors 42 onto the surface 12 as apattern 28. The surface 12 is coated with resist (not shown) whichreacts with the electron beam 40. The electron beam 22 may be directedto overlap a variable portion of an aperture 26, affecting the size andshape of the pattern 28. Blanking plates (not shown) are used to deflectthe beam 16 or the shaped beam 22 so to prevent the electron beam fromreaching the surface 12 during a period after each shot when the lensesdirecting the beam 22 and the deflectors 42 are being re-adjusted forthe succeeding shot. Typically the blanking plates are positioned so asto deflect the electron beam 16 to prevent it from illuminating aperture20. Conventionally, the blanking period may be a fixed length of time,or it may vary depending, for example, on how much the deflector 42 mustbe re-adjusted for the position of the succeeding shot.

In electron beam writer system 10, the substrate 34 is mounted on amovable platform or stage 32. The stage 32 allows substrate 34 to berepositioned so that patterns which are larger than the maximumdeflection capability or field size of the charged particle beam 40 maybe written to surface 12 in a series of subfields, where each subfieldis within the capability of deflector 42 to deflect the beam 40. In oneembodiment the substrate 34 may be a reticle. In this embodiment, thereticle, after being exposed with the pattern, undergoes variousmanufacturing steps through which it becomes a lithographic mask orphotomask. The mask may then be used in an optical lithography machineto project an image of the reticle pattern 28, generally reduced insize, onto a silicon wafer to produce an integrated circuit. Moregenerally, the mask is used in another device or machine to transfer thepattern 28 on to a substrate (not illustrated).

The minimum size pattern that can be projected with reasonable accuracyonto the surface 12 is limited by a variety of short-range physicaleffects associated with the electron beam writer system 10 and with thesurface 12, which normally comprises a resist coating on the substrate34. These effects include forward scattering, Coulomb effect, and resistdiffusion. Beam blur, also called β_(f), is a term used to include allof these short-range effects. The most modern electron beam writersystems can achieve an effective beam blur radius or β_(f) in the rangeof 20 nm to 30 nm. Forward scattering may constitute one quarter to onehalf of the total beam blur. Modern electron beam writer systems containnumerous mechanisms to reduce each of the constituent pieces of beamblur to a minimum. Since some components of beam blur are a function ofthe calibration level of a particle beam writer, the β_(f) of twoparticle beam writers of the same design may differ. The diffusioncharacteristics of resists may also vary. Variation of β_(f) based onshot size or shot dose can be simulated and systemically accounted for.But there are other effects that cannot or are not accounted for, andthey appear as random variation.

The shot dosage of a charged particle beam writer such as an electronbeam writer system is a function of the intensity of the beam source 14and the exposure time for each shot. Typically the beam intensityremains nominally fixed, and the exposure time is varied to obtainvariable shot dosages. The exposure time may be varied to compensate forvarious long-range effects such as backscatter, fogging and loadingeffects in a process called proximity effect correction (PEC). Electronbeam writer systems usually allow setting an overall dosage, called abase dosage, which affects all shots in an exposure pass. Some electronbeam writer systems perform dosage compensation calculations within theelectron beam writer system itself, and do not allow the dosage of eachshot to be assigned individually as part of the input shot list, theinput shots therefore having unassigned shot dosages. In such electronbeam writer systems, all shots implicitly have the base dosage, beforePEC. Other electron beam writer systems do allow explicit dosageassignment on a shot-by-shot basis. In electron beam writer systems thatallow shot-by-shot dosage assignment, the number of available dosagelevels may be 64 to 4096 or more, or there may be a relatively fewavailable dosage levels, such as 3 to 8 levels. For scanned multi-beamsystems, dosage adjustment may be done by scanning the surface multipletimes.

A charged particle beam system may expose a surface with a plurality ofindividually-controllable beams or beamlets. FIG. 2 illustrates anelectro-optical schematic diagram in which there are three chargedparticle beamlets 210. Associated with each beamlet 210 is a beamcontroller 220. Beam controller 220 can, for example, allow itsassociated beamlet 210 to strike surface 230, and can also preventbeamlet 210 from striking the surface 230. In some embodiments, beamcontroller 220 may also control beam blur, magnification, size and/orshape of beamlet 210. In this disclosure, a charged particle beam systemwhich has a plurality of individually-controllable beamlets is called amulti-beam system. In some embodiments, charged particles from a singlesource may be sub-divided to form a plurality of beamlets 210. In otherembodiments, a plurality of sources may be used to create the pluralityof beamlets 210. In some embodiments, beamlets 210 may be shaped by oneor more apertures, whereas in other embodiments there may be noapertures to shape the beamlets. Each beam controller 220 may allow theperiod of exposure of its associated beamlet to be controlledindividually. Generally the beamlets will be reduced in size by one ormore lenses (not shown) before striking the surface 230. In someembodiments, each beamlet may have a separate electro-optical lens,while in other embodiments a plurality of beamlets, including possiblyall beamlets, will share an electro-optical lens.

For purposes of this disclosure, a shot is the exposure of some surfacearea over a period of time. The area may be comprised of multiplediscontinuous smaller areas. A shot may be comprised of a plurality ofother shots which may or may not overlap, and which may or may not beexposed simultaneously. A shot may comprise a specified dose, or thedose may be unspecified. Shots may use a shaped beam, an unshaped beam,or a combination of shaped and unshaped beams. FIGS. 3A-3F illustratesome various types of shots. FIG. 3A illustrates an example of arectangular shot 310. A VSB charged particle beam system can, forexample, form rectangular shots in a variety of x and y dimensions. FIG.3B illustrates an example of a character projection (CP) shot 320, whichis circular in this example. FIG. 3C illustrates an example of atrapezoidal shot 330. In one embodiment, shot 330 may be a created usinga raster-scanned charged particle beam, where the beam is scanned, forexample, in the x-direction as illustrated with scan lines 332. FIG. 3Dillustrates an example of a dragged shot 340, disclosed in U.S. PatentApplication Publication 2011-0089345. Shot 340 is formed by exposing thesurface with a curvilinear shaped beam 342 at an initial referenceposition 344, and then moving the shaped beam across the surface fromposition 344 to position 346. A dragged shot path may be, for example,linear, piecewise linear, or curvilinear.

FIG. 3E illustrates an example of a shot 350 that is an array ofcircular patterns 352. Shot 350 may be formed in a variety of ways,including multiple shots of a single circular CP character, one or moreshots of a CP character which is an array of circular apertures, and oneor more multi-beam shots using circular apertures. FIG. 3F illustratesan example of a shot 360 that is a sparse array of rectangular patterns362 and 364. Shot 360 may be formed in a variety of ways, including aplurality of VSB shots, a CP shot, and one or more multi-beam shotsusing rectangular apertures. In some embodiments of multi-beam, shot 360may comprise a plurality of interleaved groups of other multi-beamshots. For example, patterns 362 may be shot simultaneously, thenpatterns 364 may be shot simultaneously at a time different frompatterns 362.

FIG. 4 illustrates an embodiment of a charged particle beam exposuresystem 400. Charged particle beam system 400 is a multi-beam system, inwhich a plurality of individually-controllable shaped beams cansimultaneously expose a surface. Multi-beam system 400 has an electronbeam source 402 that creates an electron beam 404. The electron beam 404is directed toward aperture plate 408 by condenser 406, which mayinclude electrostatic and/or magnetic elements. Aperture plate 408 has aplurality of apertures 410 which are illuminated by electron beam 404,and through which electron beam 404 passes to form a plurality of shapedbeamlets 436. In some embodiments, aperture plate 408 may have hundredsor thousands of apertures 410. Although FIG. 4 illustrates an embodimentwith a single electron beam source 402, in other embodiments apertures410 may be illuminated by electrons from a plurality of electron beamsources. Apertures 410 may be rectangular, or may be of a differentshape, for example circular. The set of beamlets 436 then illuminates ablanking controller plate 432. The blanking controller plate 432 has aplurality of blanking controllers 434, each of which is aligned with abeamlet 436. Each blanking controller 434 can individually control itsassociated beamlet 436, so as to either allow the beamlet 436 to strikesurface 424, or to prevent the beamlet 436 from striking the surface424. The amount of time for which the beam strikes the surface controlsthe total energy or “dose” applied by that beamlet. Therefore, the doseof each beamlet may be independently controlled.

In FIG. 4 beamlets that are allowed to strike surface 424 areillustrated as beamlets 412. In one embodiment, the blanking controller434 prevents its beamlet 436 from striking the surface 424 by deflectingbeamlet 436 so that it is stopped by an aperture plate 416 whichcontains an aperture 418. In some embodiments, blanking plate 432 may bedirectly adjacent to aperture plate 408. In other embodiments, therelative locations of aperture plate 408 and blanking controller 432 maybe reversed from the position illustrated in FIG. 4, so that beam 404strikes the plurality of blanking controllers 434. A system of lensescomprising elements 414, 420, and 422 allows projection of the pluralityof beamlets 412 onto surface 424 of substrate 426, typically at areduced size compared to the plurality of apertures 410. Thereduced-size beamlets form a beamlet group 440 which strikes the surface424 to form a pattern that corresponds to the pattern of the apertures410, which are allowed to strike surface 424 by blanking controllers434. In FIG. 4, beamlet group 440 has four beamlets illustrated forforming a pattern on surface 424.

Substrate 426 is positioned on movable platform or stage 428, which canbe repositioned using actuators 430. By moving stage 428, beam 440 canexpose an area larger than the dimensions of the maximum size patternformed by beamlet group 440, using a plurality of exposures or shots. Insome embodiments, the stage 428 remains stationary during an exposure,and is then repositioned for a subsequent exposure. In otherembodiments, stage 428 moves continuously and at a variable velocity. Inyet other embodiments, stage 428 moves continuously but at a constantvelocity, which can increase the accuracy of the stage positioning. Forthose embodiments in which stage 428 moves continuously, a set ofdeflectors (not shown) may be used to move the beam to match thedirection and velocity of stage 428, allowing the beamlet group 440 toremain stationary with respect to surface 424 during an exposure. Instill other embodiments of multi-beam systems, individual beamlets in abeamlet group may be deflected across surface 424 independently fromother beamlets in the beamlet group.

Other types of multi-beam systems may create a plurality of unshapedbeamlets 436, such as by using a plurality of charged particle beamsources to create an array of Gaussian beamlets.

Conventional Bias Correction

In the process of manufacturing a pattern on a surface, it is desirableto control the widths of shapes projected onto the surface by being ableto provide a given constant bias. For example, often, one “mask” ismade, then it might be determined that for whatever reason the patternfeatures on it are slightly too thick or too thin, say by 2.3 nm. Thefabricator would then desire to bias all the edges in the pattern by 2.3nm/2=1.65 nm in another iteration to create the next better version.Constant bias is illustrated in FIG. 5. FIG. 5 shows an example pattern510 comprising the text “Hello World”. Pattern 520 is similar to theoriginal pattern 510, but where the edges which have been positivelybiased in pattern 520—i.e. the edges have been moved outward—so that theletters are thicker. In biasing, the edges of each figure in a patternare biased “inwards” or “outwards,” to make the width of each patternnarrower or fatter. The scale of the pattern does not change. Biasingmay be performed, for example, to account for changes in etchingcharacteristics (over-etching or under-etching).

FIG. 6 illustrates a conventional method of producing bias, by biasingthe input CAD (computer-aided design) shapes geometrically. Element 610is an original pattern, in the shape of an “H”. Vectors 620 illustratethe direction in which each edge portion of pattern 610 is to moveduring positive biasing. Element 612 illustrates the revised patternafter a positive bias. Performing the biasing on shapes is a complexoperation:

-   -   Positive biasing—outward biasing—can create overlaps, which must        be eliminated in a post-processing step.    -   Negative biasing—inward biasing—can cause narrow areas to        disappear.    -   Positive biasing, done correctly, causes square corners to        become rounded. Curvilinear shapes are difficult to represent        and process in most CAD systems.    -   The resulting output file is usually larger than the input file,        and requires significant time to write and to subsequently read        from, for example, a computer disk.

This geometric method is not popular, because of the substantialcomputational effort required to bias the CAD shapes, and the consequenteffect on mask turnaround time.

In a variant of the above method, the CAD shapes may be biased as theyare read into a mask exposure system. Doing this saves disk input/output(I/O) volume, reducing or eliminating the turnaround time issue.However, this method still has the problem that a geometric constantbias is often not the only correction that is desired.

Another known correction method is to bias the dose of the source. Ifall shapes have a similar dose margin (i.e., edge slope), a desiredconstant distance bias can be obtained by changing the dose delivered tothe surface. This has been the predominant method of biasing. Thecurrent method works well when dose margin is a good proxy for allsources of manufacturing variation. There are situations where constantbias in width is desirable. The current method does not work to createbias that is uniform in bias width, except when the following conditionsare satisfied:

-   -   Minimum shape dimensions are fairly large when compared to the        forward blur of the writing process, such as ≥100 nm (mask        coordinates) for the leading edge mask processes in        semiconductor device manufacturing.    -   All shots were “normal” dosage—also called 1.0—before correction        for long-range effects.    -   Shots do not overlap, since shot overlap creates areas of        differing dosage.    -   The amount of backscatter provided by adjacent shots, typically        within about a 10-30 um range for a leading edge photomask for        semiconductor devices, is relatively constant across the entire        surface.        Short-range effects cause some non-uniformity in biasing, but        with fairly large shots this has been acceptable.

In the most advanced masks, however, some or all of these conditions maybe violated:

-   -   Minimum shape dimensions are small, such as less than 100 nm in        mask coordinates for electron beam lithography.    -   Shots have varying dosages.    -   Shot may overlap.    -   10-30 um scale local density may vary significantly across the        surface.        In this environment, a dosage change does not produce constant        distance biasing.

FIGS. 7, 8, 9 and 10 show the results of simulating a 5% dosage biasaccording to conventional methods, with shapes of differing sizes, andstarting with different exposure dosages, with electron beam exposure.FIG. 7 presents the conditions of the simulation, which was done usingtwo long shots: one shot with a width of 30 nm and one shot with a widthof 200 nm. The following simulation conditions were used:

-   -   Forward sigma of 20 nm. This simulates forward scattering and        other effects which are collectively referred to as “beam blur.”    -   PEC: Pattern density ISO, meaning that the lines is isolated,        for the purposes of proximity effect correction (PEC). As in        known to those skilled in the art, PEC corrects for backward        scattering and other long range effects.    -   Two dosages for VSB shots: 1.0 and 2.0.        There are therefore four simulations: two shape widths at each        of two dosages. FIG. 8 presents the results of the simulation.    -   “Dose” column: The shot dosage, assuming a 0.5 threshold.    -   “TargetCD”: The two desired pattern widths of 30 nm and 200 nm.    -   “ShotSize”: The actual shot size. As can be seen, for 1.0 dose,        the shot size is the same as the TargetCD. For 2.0 dose, the        shots must be made narrower to achieve the TargetCD.    -   “Output CD”: The simulated CD achieved with the specified shot        width and shot dose. Note that the 30 nm wide shot does not        produce a 30 nm wide pattern at a 1.0 dose, due to the small        shot size.    -   “Dose Margin/Edge Slope”: The calculated dose margin at the        pattern edge.    -   “Delta CD from 5% Dose Biasing”: This is the change in pattern        width that would be produced by changing the dosage 5%.        As can be seen from FIG. 8, the change in dimension (Delta CD)        from the 5% dose biasing varies between the 30 nm and 200 nm        wide shapes, and also between the 1.0 and 2.0 dosages. This        illustrates that dose biasing does not provide a constant        distance dimensional change across the conditions of the        simulation.

FIG. 9 illustrates dosage profiles for the 200 nm shape, for 1.0 dose,1.05 dose, 2.0 dose, and 2.1 dose (2.0*105%). Curve 910 is the dosageprofile for 1.0 dose; curve 920 is the dosage profile for 1.05 dose(1.0*105%); curve 930 is the dosage profile for 2.0 dose; and curve 940is the dosage profile for 2.1 dose (2.0*105%). FIG. 10 illustrates thesame dosage profiles as FIG. 9, but zoomed in near the 200 nm/0.5(threshold) dosage point. Point 950 indicates that the 1.0 and 2.0 doses(curves 910 and 930, respectively) cross the 0.5 threshold value at anx-coordinate of 200 nm. Point 955 indicates that both the 1× and 2×doses with 5% bias (curves 920 and 940, respectively) have doses of1.05*0.5=0.525 at the pre-bias contour (x=200 nm). Thus, for both the1.05 dosage curve 920 and for the 2.1 dosage curve 940, the dose at anx-coordinate of 200 nm is 5% above the 0.5 threshold value at anx-coordinate of 200 nm. The 5% dose increase at an x-coordinate of 200nm has therefore been achieved. The amount the edge will move with a 5%dose is determined by where the curve crosses the threshold value of0.5. Curve 920 intersects dose=0.5 at x-coordinate 960. Curve 940, whichhas a higher slope than curve 920, intersects dose=0.5 at x-coordinate970, which is closer to x-coordinate 200 nm than is x-coordinate 960.Constant biasing is therefore not achieved.

Thus, improved methods of bias correction are needed.

Improved Bias Correction

The present disclosure shall apply to manufacturing patterns using amulti-beam energy source, on any surface such as a mask, wafer, flatpanel display (FPD), or FPD mask. The types of energy sources includeelectron beam (eBeam), proton beam, argon fluoride (ArF) optical laser,multi-frequency lasers (as FPD writers use), and EUV. In multi-beam, asingle chamber (often called the column) houses an apparatus that shootsmultiple shapes simultaneously either through a single source (e.g.,electron gun or light source) or through multiple sources. Multipleshapes may be an array of, for example, 512×512, but can be any numbersuch as ranging from a total of approximately 10 or less, to much morethan 512×512. These shapes, which may be squares, are referred to aspixels in this disclosure.

Embodiments utilize a multi-beam machine to modify the dose ofindividual pixels to bring about a constant distance bias for every edgeof every shape for the whole mask. This can be done inline within themachine, for example by using graphics processing unit (GPU)acceleration for the computing. By computing the simulated effect of adose change of the pixels, every edge can be biased by approximatelyplus or minus a portion of the pixel size, while also manipulating thedose profile to enhance dose margin in various ways. The implementationmay involve, for example, less than a pixel of bias, such as half apixel. Larger biases with more complex analyses are also possible.“Enhancing” or improving dose margin is thought of as increasing doseslope (making it steeper) so that it is less susceptible tomanufacturing variation. Since calculations for many pixels can be donein parallel, special purpose hardware devices may be used to improveperformance over general purpose CPUs. In some embodiments, the specialpurpose hardware device may be a graphical processing unit (GPU).

Improving the uniformity of dose margins across the mask is an importantagenda for mask shops. This has been because mask shops in somesituations want to modify dose to achieve a relatively constant edgebias for all shapes in the mask. The present methods offer a superioralternative to that methodology in providing a way to achieve edge biascorrection without any turnaround time penalty of another iteration ofCAD.

In FIG. 11, shaded quarter circle 1110 represents a section of a patternto be written onto a surface. Each pattern has at least one edge, suchthat a plurality of patterns for a surface has a plurality of edges. Thequarter circle 1110 portion of the pattern comprises edge 1120. As canbe seen in the example of FIG. 11, a pattern may cover fractionalportions of pixels 1130 in the array of pixels. Each pixel 1130 has acorresponding dose. In this example, the dose for pixels fully coveredby the pattern is 1.0; doses for pixels at or near an edge of thepattern have a non-zero fractional amount (e.g., 0.05 to 0.9); andpixels that are outside of the pattern or pattern edge have a dose ofzero. The pixel coverage can be used to generate the location of thedesired edge within each pixel, as well as the local dose slopegradient.

FIG. 12A illustrates rasterization of a portion of a surface into agrid, or array, of pixels. Pixels are typically 10 nm, although they maybe 7 nm, 20 nm, or any other size. The values illustrated in each pixelof the FIG. 12A grid represent dosage values to be exposed onto thesurface from FIG. 11 pattern 1110. In this example, the dose thresholdis 0.5.

Using the pixel array of FIG. 12A, a shape edge can be calculated. Insome embodiments, interpolation can be used to determine the x and ycoordinates where dosage crosses the dose threshold. For each specifiedpixel in which an edge of a pattern has been identified, a location andan orientation of the identified edge is determined. FIG. 12Billustrates the pixel array of FIG. 12A, with identified edge 1220 alsoillustrated. Desirably, calculation of identified edge 1220 can be doneusing dosages only from pixels in the neighborhood of the edge, whichfacilitates parallel processing in doing the calculations. Theneighborhood of the edge may be, for example, within 1-5 pixels awayfrom the edge.

Knowing the shape edge 1220, the mathematical gradient of this edge maybe calculated at any point on the edge. FIG. 13A graphically illustratesthe gradient vectors 1310 extending from edge 1220, in the direction ofa positive bias. For negative bias, each gradient vector would point inan opposite direction.

FIG. 13B illustrates the pixel array, where pixel dosages have beencalculated to relocate edge 1220 by the target bias amount, to position1320.

The calculations described above are repeated for each pixel near any ofthe plurality of edges in the plurality of patterns. As indicated in theabove example, calculations required for edge biasing using pixel dosagearrays can be done for each pixel using dosage information for onlynearby pixels. This allows parallel processing of calculations. In someembodiments, the parallel processing may comprise use of graphicalprocessing units (GPUs) or other specialized hardware.

Dose margin enhancement can also be accomplished with pixel dosage arrayshape data. As is known to those skilled in the art, in a leading edgemask process in semiconductor device manufacturing, for example, whenshapes smaller than approximately 100 nm in mask dimensions are exposedwith a normal 1.0 dose shot, the edge will have a lower dose margin thanfor larger shots. FIGS. 14-16 illustrate how biasing can be combinedwith dose margin enhancement. FIG. 14 illustrates an example pixel dosearray 1400 to be exposed using an electron beam exposure system. In thisexample, the pixel size is 10 nm in both X and Y directions. Acalculated edge 1410 is determined from this data, representing a lineend pattern. As shown in FIG. 14, the width of the line end pattern inthis example is 70 nm.

FIG. 15 a pixel array in which pixel dosages have been calculated tonegatively bias edge 1410, relocating it to position 1510. The biasedpattern with edge position 1510 has a width of 60 nm, using a targetbias of 10 nm from the original 70 nm width. The maximum pixel dosage is1.0. Pixel 1520, for example, through which the target edge traverses,has a dosage of 0.5. As is known to those skilled in the art, a 60 nmwide line end pattern exposed with a normal 1.0 dose will have anundesirably low dose margin because of the characteristics of electronbeam exposure systems when exposing patterns which are this small.

Dose margin can be improved by increasing the dose of pixels near edge1510, as illustrated in FIG. 16. In pixel array 1600 of FIG. 16, themaximum pixel dosage is set to 1.3, meaning 1.3 time a normal dose.Pixel array 1600 has a higher dose margin for the biased edge 1510 thandoes pixel array 1500. In pixel array 1600, pixels in the center of theline end pattern remain at 1.0 dose, since increasing the dose of thesepixels is less effective at improving dose margin than providingincreased dosage closer to the edge 1510. Pixel 1620, which correspondsto FIG. 15 pixel 1520, has a dose of 0.2—less than pixel 1520, which isnecessary to maintain the target edge with the adjacent interior pixelhaving a dose of 1.3.

In the example of FIG. 16, the maximum pixel dosage is 1.3. Use of evenhigher pixel dosages can further improve dose margin. However, in somemulti-beam exposure systems, the exposure time for the surface isdetermined by the maximum dosage pixel(s) in the pattern. Higher maximumpixel dosages lengthen the overall exposure time, increasing turnaroundtime and cost.

FIG. 17 illustrates an example flowchart for performing biascorrections, in accordance with some embodiments. The input is a set ofshapes 1705, such as from a computer-aided design (CAD) system. The setof shapes 1705 may be a plurality of patterns, for example, a set ofgeometric shapes. Each pattern in the plurality of patterns has an edge.In step 1710, the input shapes are rasterized by determining the pixeldoses in a 2-dimensional array of pixels, using the plurality ofpatterns, to create a 2-dimensional array of dosages 1715 whichrepresent dosages for a pixelized representation of a surface to beexposed. Each pixel in the array of pixels represents an exposuredosage. The pattern data of the plurality of patterns—e.g., thegeometric shape data of the patterns—is rasterized to create the arrayof pixels. Using the array 1715, in step 1720 the edges of the patternsare identified, and the gradient vectors along each of the edges arecalculated. Identification of the edges in step 1720 may includecalculating a location of the edge using pixel dosages of the array ofpixels. Step 1720 also uses as input the target bias 1780. The directionof the gradient vectors is determined by whether the desired bias ispositive (outward) or negative (inward).

In step 1730 pixel dosages are calculated which will cause edges to berelocated by the target bias 1780. Step 1730 uses as input the array1715 and the target bias 1780. Additionally, step 1730 may input apredetermined maximum pixel dose 1735. In some embodiments, step 1730includes calculating the dose margin of each relocated edge, andadjusting pixel dosages to increase the dose margin in locations wherethe dose margin is less than a pre-determined minimum acceptable value.For example, the dose margin may be improved by increasing the pixeldose of a pixel near the relocated edge. The dose margin may bemaximized, within a constraint of a predetermined maximum pixel dose, orit may be improved to at least a predetermined minimum dose margin. Inother embodiments, step 1730 includes maximizing the dose margin of eachedge, subject to the maximum pixel dose. In some embodiments, step 1730may also include correction for non-linearities in the exposure systemhardware. Step 1730 outputs dosage array 1740, which is the array ofpixels with the calculated pixel dosages. In step 1745, a surface isexposed in a multi-beam exposure system using the dosage array 1740.

In some embodiments, calculating the calculated pixel dose in step 1730can include compensating for a mid-range scattering. In one embodiment,mid-range exposure effects are calculated in step 1750 from dosage array1715. Step 1750 outputs a mid-range dosage array 1755. The mid-rangedosage array 1755 may be coarser than array 1715—i.e. each pixel inarray 1755 represents a larger area than in dosage array 1715. In step1730, dosage from a pixel in mid-range dose array 1755 is subtractedfrom each calculated pixel dosage before outputting the dosage to array1740.

Other quantities at the edges of the patterns can be adjusted using thesame pixel methodology, such as compensating for eBeam non-linearity.

As described above, in the present methods all the calculations for thebias are local. Ordinarily, to do this sort of biasing geometrically,one would first need to analyze and combine the various geometricprimitives together, which is an expensive operation. In contrast, byperforming the biasing after the geometric data has been rasterized intopixels as in the present methods, it is possible to perform the biasingas a set of small local calculations, modifying each pixel based onnothing more than its immediate neighbors. Such local calculationsenable the processing to be parallelized. In some embodiments,calculations may be performed in real time as an inline process, duringthe exposure of the surface by a multi-beam exposure system. In otherembodiments, calculations may be performed during the exposure ofanother surface, in a pipelined fashion. In a pipelined system, the nextsurface to be written on the machine is calculated while the previoussurface is being written on the machine. A pipelined system is effectivefor improving the throughput of many surfaces, if the surfaces havesimilar write times and compute times. An inline (real time) system iseffective for improving the throughput as well as the turnaround timesof each surface.

The present methods can be used offline, pipelined, or inline. Beingfast enough to be able to process inline is most desirable. Inlineprocessing is most desirable particularly when the number of totalpixels that needs to be written is very large. For example, forsemiconductor device manufacturing for multi-beam eBeam writing ofmasks, over 500 T-Bytes of data are required to store all the pixeldata. Since multi-beam eBeam machines need to write the pixels extremelyquickly, storing such data on hard disk or even solid state disk may notbe practical in cost. In inline processing, unlike in offline orpipelined processing, there is no need to store the data because themachine consumes the data to write the pixels soon after the data iscomputed. This is another reason why inline processing that the presentmethods enable is valuable. As mentioned above, the same methodology canbe used for adjusting pixel doses to improve dose margin (i.e., edgeslope).

The calculations described or referred to in this disclosure may beaccomplished in various ways. Due to the large amount of calculationsrequired, multiple computers or processor cores of a CPU may also beused in parallel. In one embodiment, the computations may be subdividedinto a plurality of 2-dimensional geometric regions for one or morecomputation-intensive steps in the flow, to support parallel processing.In another embodiment, a special-purpose hardware device, either usedsingly or in multiples, may be used to perform the computations of oneor more steps with greater speed than using general-purpose computers orprocessor cores. Specialty computing hardware devices or processors mayinclude, for example, field-programmable gate arrays (FPGA),application-specific integrated circuits (ASIC), or digital signalprocessor (DSP) chips. In one embodiment, the special-purpose hardwaredevice may be a graphics processing unit (GPU). In another embodiment,the optimization and simulation processes described in this disclosuremay include iterative processes of revising and recalculating possiblesolutions. In yet another embodiment, calculations may be performed in acorrect-by-construction method, so that no iterations are required.

FIG. 18 illustrates an example of a computing hardware device 1800 thatmay be used to perform the calculations described in this disclosure.Computing hardware device 1800 comprises a central processing unit (CPU)1802, with attached main memory 1804. The CPU may comprise, for example,eight processing cores, thereby enhancing performance of any parts ofthe computer software that are multi-threaded. The size of main memory1804 may be, for example, 64 G-bytes. The CPU 1802 is connected to aPeripheral Component Interconnect Express (PCIe) bus 1820. A graphicsprocessing unit (GPU) 1814 is also connected to the PCIe bus. Incomputing hardware device 1800, the GPU 1814 may or may not be connectedto a graphics output device such as a video monitor. If not connected toa graphics output device, GPU 1814 may be used purely as a high-speedparallel computation engine. The computing software may obtainsignificantly-higher performance by using the GPU for a portion of thecalculations, compared to using CPU 1802 for all the calculations. TheCPU 1802 communicates with the GPU 1814 via PCIe bus 1820. In otherembodiments (not illustrated) GPU 1814 may be integrated with CPU 1802,rather than being connected to PCIe bus 1820. Disk controller 1808 mayalso be attached to the PCIe bus, with, for example, two disks 1810connected to disk controller 1808. Finally, a local area network (LAN)controller 1812 may also be attached to the PCIe bus, and providesGigabit Ethernet (GbE) connectivity to other computers. In someembodiments, the computer software and/or the design data are stored ondisks 1810. In other embodiments, either the computer programs or thedesign data or both the computer programs and the design data may beaccessed from other computers or file serving hardware via the GbEEthernet.

In some embodiments, a system for biasing shapes to be written onto asurface includes a device configured to input an array of pixels. Eachpixel comprises a pixel dose, and the array of pixels represents dosageon a surface to be exposed with a plurality of patterns. Each pattern ofthe plurality of patterns has an edge. The system also includes a deviceconfigured to identify an edge of a pattern in the plurality ofpatterns; a device configured to calculate a calculated pixel dose forpixels which are in a neighborhood of the identified edge, so that theidentified edge is relocated by a target bias; and a device configuredto output the array of pixels with the calculated pixel doses. In someembodiments, the system includes a device configured to determine thedosages in the pixel array, using a set of geometric shapes. In someembodiments, the system can also include a device configured to exposethe surface with the outputted array of pixels. The device configured tocalculate the pixel doses may operate simultaneously with the deviceconfigured to expose the surface, in an inline fashion. The deviceconfigured to expose the surface may comprise multiple beams.

In some embodiments, a system includes a device configured to expose apattern onto a resist-coated surface using an electron beam, and adevice configured to compute a constant distance bias. The deviceconfigured to expose may expose the resist of the resist-coated surfacewith multiple beams. The device configured to expose and the deviceconfigured to compute may operate in an inline fashion. The deviceconfigured to compute may comprise a graphics processing unit (GPU).

Reference has been made in detail to embodiments of the disclosedinvention, one or more examples of which have been illustrated in theaccompanying figures. Each example has been provided by way ofexplanation of the present technology, not as a limitation of thepresent technology. In fact, while the specification has been describedin detail with respect to specific embodiments of the invention, it willbe appreciated that those skilled in the art, upon attaining anunderstanding of the foregoing, may readily conceive of alterations to,variations of, and equivalents to these embodiments. For instance,features illustrated or described as part of one embodiment may be usedwith another embodiment to yield a still further embodiment. Thus, it isintended that the present subject matter covers all such modificationsand variations within the scope of the appended claims and theirequivalents. These and other modifications and variations to the presentinvention may be practiced by those of ordinary skill in the art,without departing from the scope of the present invention, which is moreparticularly set forth in the appended claims. Furthermore, those ofordinary skill in the art will appreciate that the foregoing descriptionis by way of example only, and is not intended to limit the invention.

What is claimed is:
 1. A system for biasing shapes to be written onto asurface, the system comprising: a device configured to input an array ofpixels, wherein each pixel comprises a pixel dose, and wherein the arrayof pixels represents dosage on a surface to be exposed with a pluralityof patterns, each pattern of the plurality of patterns comprising anedge; a device configured to identify the edge of a pattern in theplurality of patterns, wherein the edge location may be identifiedwithin a fractional portion of each pixel; a device configured tocalculate a calculated pixel dose for pixels which are in a neighborhoodof the identified edge, so that the identified edge is relocated by atarget bias, wherein calculating the calculated pixel dose comprises asimulated effect of a dose change; and a device configured to output thearray of pixels with the calculated pixel doses.
 2. The system of claim1, further comprising a device configured to determine the pixel dosesin the array of pixels, using a set of geometric shapes.
 3. The systemof claim 1, further comprising a device configured to expose the surfacewith the outputted array of pixels.
 4. The system of claim 3 wherein thedevice configured to calculate the calculated pixel doses operatessimultaneously with the device configured to expose the surface, in aninline fashion.
 5. The system of claim 3 wherein the device configuredto expose the surface comprises multiple beams.
 6. A system comprising:a device configured to expose a pattern onto a resist-coated surfaceusing an electron beam; and a device configured to compute a constantdistance bias.
 7. The system of claim 6 wherein the device configured toexpose exposes the resist-coated surface with multiple beams.
 8. Thesystem of claim 6 wherein the device configured to expose and the deviceconfigured to compute operate in an inline fashion.
 9. The system ofclaim 6 wherein the device configured to compute comprises a graphicsprocessing unit (GPU).